A footnote to a paper by Ionescu
Let X be a complex projective manifold of dimension \(d\geq 3\), polarized by an ample line bundle H and let \(K_ X\) stand for its canonical bundle. A recent result by \textit{P. Ionescu} [''Generalized adjunction and applications'', Prepr. Ser. Math., Bucuresti 48 (1985)] strongly bounds the dimension of the exceptional locus of the contraction of a non numerically effective extremal ray on X. By using this the ampleness of \(K_ X\otimes H^{d-2W}\) and the semi-ampleness of \(K_ X\otimes H^{d-3} (d\geq 4)\) are studied. Ionescu himself had already described the cases when \(K_ X\otimes H^ t\) is not semi-ample for \(t=d-2, d-1, d\) and is not ample for \(t=d-1, d\). Note also that some of the above results are contained in a recent paper by Fujita. Both Ionescu's paper and Fujita's are quoted in the reference.
scientific article; zbMATH DE number 4008538
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